Definition:Contingency Table

Definition

A contingency table is an array of $r$ rows and $c$ columns in which:

each row and each column is associated with a specific attribute

the number $n_{i j}$ in row $i$ and column $j$ is a count of the number of units having that combination of attributes.

It is then commonplace to perform a chi-squared test to investigate how the data may differ between categories.

Row and column categories may be either nominal or ordinal.

Cell

The element in row $i$ and column $j$ of a contingency table is referred to as cell $\tuple {i, j}$ of that contingency table.

Marginal Total

The marginal totals of a contingency table are the totals of each of the rows and columns of that contingency table.

Examples

Arbitrary Example

The following is an example of a contingency table:

$\begin{array}{r|ccc|c} & \text {Superior} & \text {Average} & \text {Poor} & \text {Factory totals} \\ \hline \text {Factory A} & 12 & 20 & 8 & 40 \\ \text {Factory B} & 14 & 39 & 7 & 60 \\ \hline \text {Category totals} & 26 & 59 & 15 \end{array}$

Also see

• Results about contingency tables can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): contingency table
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): contingency table